Following several rocket attacks on Israel in the last few hours, the IAF resumed air strikes on terrorist targets across the Gaza Strip, the IDF said.
After a quiet night between the borders, which saw no rockets fired into Israel and no IDF fire in Gaza, rocket fire renewed with rocket sirens sounding throughout Hof Ashkelon Regional Council as well as the Sdot Negev Regional Council.
One rocket was found to have landed in an open area and no damages were reported. The rocket fire continued into the afternoon.
Gaza medical officials said that two people, including a child, were killed by Israeli fire in the northern Gaza Strip on Monday.
The IDF did not confirm the reports.
The Cabinet held a special session on Monday morning to discuss the continuation of the operation and whether to end or expand the offensive.
A new policy of holding fire from ground and air in Gaza, unless provoked, does not apply to the tunnels built by Hamas terrorists, however. Forces are still working to destroy them, the IDF says.
Army Radio reported that overnight Sunday, the IDF destroyed two tunnels. The report also quotes sources as saying the current situation is an "unlimited cease-fire," in which Israel will only hit targets when provoked.
IDF spokesperson Moti Almoz told Army Radio on Monday morning that the "unlimited cease-fire means that we are prepared for the continuation of actions but are currently focused on the tunnels, and there are a few more that we need to work on."
On Sunday night, US President Barack Obama told Prime Minister Benyamin Netanyahu in a phone call that an immediate and unconditional ceasefire ending Israel's assault on Hamas is a "clear strategic imperative" to Israel.
While the conversation between the leaders focused on the immediate concerns of the United States, the president also discussed the broader implications of Israel's operation in Gaza, Protective Edge, now over two weeks old and burdened with a mounting death toll, both within the Israel Defense Forces and the civilian population of Gaza.
Yaakov Lappin and Michael Wilner contributed to this report.